Hypothesis Test for Proportions

The null hypothesis is represented by:

• Ha

• Ho

• t*

• HP

• μ

Tags

CCSS.HSS.IC.B.3

The null hypothesis always contains a(an):

• < or >

• =

• >

• = or >

• ≠

When p-value is greater than alpha we:

• Accept Ho
• Accept Ha
• Fail to reject Ho
• Reject Ho

What does it mean when a test is statistically significant?

• it has reached alpha level status
• the test statistic had a P-value higher than the alpha level
• the test statistic had a P-value lower than the alpha level
• it is important in practical terms

This is the same write-up as found in the previous question:

A recent newspaper article claimed that the President’s approval rating is 46%; however, a sample of 80 U.S. citizens shows that 43 of them approve of the President’s performance. At a 0.10 level of significance, you are interested in determining if there is evidence that the President’s approval rating is actually higher.

What is the p-value for this hypothesis test?

• .082

• .164

• .702

• .298

Tags

CCSS.HSS.ID.A.4

Sally reads a newspaper report claiming that 12% of all adults in the U.S. are left-handed. She decides to test this claim. Sally selects a random sample of 55 classmates and finds that 9 were left-handed. Does this provide sufficient evidence that the proportion of lefties in Sally’s school is different than the national figure? Use α = 0.01.

Which is the correct p-value for this test?

• 0.160

• 0.319

• 0.508

• 0.492

The process of making cough drops yields drops with varying amounts of the active ingredient. It is claimed that the average amount of this ingredient per tablet is at least 400mg. We test a random sample of 90 tablets. The mean content of the active ingredient for the sample is 396.8mg, while the standard deviation is 31mg. What is the approximate p-value for the appropriate test?

• 0.050

• 0.100

• 0.165

• 0.330

• 0.335

The mean monthly rent for one bedroom apartments in college towns around Michigan is $900. A future student group thinks that the rent is actually higher than the claim. To help them budget, the students determine the mean monthly rent of 200 different one bedroom apartments from around Michigan. State the null and alternative hypothesis for this test.

Suppose the P-value for a hypothesis test is 0.0304. Using a = 0.05, what is the appropriate conclusion?

• a) Reject the null hypothesis

• b) Reject the alternative hypothesis

• c) Fail to reject the null hypothesis

• d) Fail to reject the alternative hypothesis

A P-value indicates:

• the probability that the null hypothesis is true
• the probability that the alternative hypothesis is true
• the probability of obtaining the results (or one more extreme) if the null hypothesis is true
• probability of a Type I error